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Proof step 2 from proof zero-ge-add-02 (previous step)

i * j0 + j * j0 < j0, i * j0 + j * j0 < 0, 0 < j0, 0 ≤ i + j, (i * j0 + j * j0) + 1 < j0 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: dist-lsplit seq: ⊦ (i + i0) * j = i * j + i0 * j subst: [i0, j, i] → [j, j0, i] flags: rewrite, current

Additional information

Used simplifier rules: ls-same: ⊦ 0 < i → (i * j < i ↔ j < 1);%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%zero-ls: ⊦ 0 < i → (i * j < 0 ↔ j < 0);%bet-01: ⊦ 0 ≤ i → (i < 1 ↔ i = 0); from specification int-abs%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs Used terms: j, j0, i